document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1138948>Question 1138948</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The monthly revenue R achieved by selling x wristwatches is figured to be <BR>\n" );
document.write( "R(x)=75x−0.2x^2.  The monthly cost C of selling x wristwatches is C(x)=28x+1650.<BR>\n" );
document.write( "​(a) How many wristwatches must the firm sell to maximize​ revenue? What is the maximum​ revenue?<BR>\n" );
document.write( "​(b) Profit is given as P(x)=R(x)−C(x). What is the profit​ function?<BR>\n" );
document.write( "​(c) How many wristwatches must the firm sell to maximize​ profit? What is the maximum​ profit?<BR>\n" );
document.write( "​(d) Provide a reasonable explanation as to why the answers found in parts​ (a) and​ (c) differ. Explain why a quadratic function is a reasonable model for revenue. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #756753 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=756753\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Revenue=75x-0.2x^2<BR>\n" );
document.write( "this is a quadratic with maximum at vertex where x=-b/2a=-75/-0.4=187.5 <BR>\n" );
document.write( "maximum revenue is $7031.20 for both 187 and 188 watches. <BR>\n" );
document.write( "profit is the difference between these two, or -0.2x^2+47x-1650<BR>\n" );
document.write( "This is maximized for x=-47/-0.4 or 117.5 watches<BR>\n" );
document.write( "f(117.5)=$1111.25\r<BR>\n" );
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document.write( "they differ because there are two different quadratics, basically.  The third graph has a difference between the two. Cost increases linearly, revenue will increase up to a point where beyond which more being sold and then decrease, either because of decrease in demand, oversupply, or other factors.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C150%2C-100%2C2000%2C-.2x%5E2%2B47x-1650%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C150%2C-100%2C2000%2C-.2x%5E2%2B47x-1650%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C220%2C-500%2C10000%2C75x-0.2x%5E2%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C220%2C-500%2C10000%2C75x-0.2x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C220%2C-2000%2C10000%2C75x-0.2x%5E2%2C28x%2B1650%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C220%2C-2000%2C10000%2C75x-0.2x%5E2%2C28x%2B1650%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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